The degree of a finite semigroup S is the minimum n such that S can be faithfully represented by transformations of an n-set. This talk will discuss some recent work calculating degrees of various classes of semigroups, including null semigroups, nilpotent semigroups, rectangular bands and sandwich semigroups. Some interesting combinatorial objects play an important role, including integer compositions and hypergraph colourings.
This is joint work with Peter Cameron, Des FitzGerald, James Mitchell, Luke Pebody and Thomas Quinn-Gregson.
This video was uploaded to YouTube by Newcastle University, Australia. It is part of the 64th annual meeting of the Australian Mathematical Society, which was held (virtually) at the University of New England.
